# The sum of two numbers is 6. If twice the smaller number is subtracted from the larger number the result is 11. How do you find the two numbers?

Mar 25, 2018

The two numbers are $\frac{23}{3}$ and $- \frac{5}{3}$

#### Explanation:

Write a system of equations, letting the two numbers be $a$ and $b$ (or whatever two variables you wish).

$\left\{\begin{matrix}a + b = 6 \\ b - 2 a = 11\end{matrix}\right.$

There are a couple of ways to solve this. We can either solve for one of the variables in one of the equations and substitute into the other equation. Or we can subtract the second equation from the first. I will do the latter but both methods arrive at the same answer.

$3 a = - 5$

$a = - \frac{5}{3}$

We know that $a + b = 6 \to b = 6 + \frac{5}{3} = \frac{23}{3}$

Hopefully this helps!